The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. The problem often arises in resource allocation where the decision makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively.

The knapsack problem has been studied for more than a century, with early works dating as far back as 1897.[1] The name "knapsack problem" dates back to the early works of the mathematician Tobias Dantzig (1884–1956),[2] and refers to the commonplace problem of packing the most valuable or useful items without overloading the luggage.

[1] Mathews, G. B. (25 June 1897). "On the partition of numbers" (PDF). Proceedings of the London Mathematical Society. 28: 486–490. doi:10.1112/plms/s1-28.1.486. [2] Dantzig, Tobias. Numbers: The Language of Science, 1930

See more about the Knapsack Problem: https://en.wikipedia.org/wiki/Knapsack_problem